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\contentsline {chapter}{Lista de Figuras}{vi}
\contentsline {chapter}{Lista de Tabelas}{vii}
\contentsline {chapter}{S\IeC {\'\i }mbolos e abrevia\c c\~oes}{xi}
\contentsline {chapter}{\numberline {1}Introdu\c c\~ao}{3}
\contentsline {section}{\numberline {1.1}Vis\~ao geral}{3}
\contentsline {section}{\numberline {1.2}Motiva\c c\~oes}{4}
\contentsline {section}{\numberline {1.3}Contribui\c c\~oes}{5}
\contentsline {section}{\numberline {1.4}Descri\c c\~ao dos cap\IeC {\'\i }tulos}{6}
\contentsline {chapter}{\numberline {2}Aprendizagem estat\IeC {\'\i }stica}{9}
\contentsline {section}{\numberline {2.1}Introdu\c c\~ao}{9}
\contentsline {section}{\numberline {2.2}Aprendizagem de m\'aquina}{9}
\contentsline {section}{\numberline {2.3}Processo de aprendizagem}{11}
\contentsline {section}{\numberline {2.4}Funcional risco}{11}
\contentsline {section}{\numberline {2.5}Princ\IeC {\'\i }pio de minimiza\c c\~ao do risco emp\IeC {\'\i }rico}{13}
\contentsline {section}{\numberline {2.6}Dimens\~ao VC}{15}
\contentsline {section}{\numberline {2.7}Princ\IeC {\'\i }pio de minimiza\c c\~ao do risco estrutural}{17}
\contentsline {section}{\numberline {2.8}Conclus\~ao}{19}
\contentsline {chapter}{\numberline {3}Support Vector Machines para classifica\c c\~ao}{21}
\contentsline {section}{\numberline {3.1}Introdu\c c\~ao}{21}
\contentsline {section}{\numberline {3.2}SVMs com margens r\IeC {\'\i }gidas}{22}
\contentsline {section}{\numberline {3.3}SVMs com margens flex\IeC {\'\i }veis}{25}
\contentsline {section}{\numberline {3.4}Mapeamento impl\IeC {\'\i }cito}{27}
\contentsline {section}{\numberline {3.5}Exemplo}{29}
\contentsline {section}{\numberline {3.6}Conclus\~ao}{30}
\contentsline {chapter}{\numberline {4}Treinando SVMs}{33}
\contentsline {section}{\numberline {4.1}Introdu\c c\~ao}{33}
\contentsline {section}{\numberline {4.2}Condi\c c\~oes de optimalidade e regi\~ao fact\IeC {\'\i }vel}{34}
\contentsline {section}{\numberline {4.3}M\'etodos de treinamento para SVMs}{35}
\contentsline {subsection}{\numberline {4.3.1}M\'etodos cl\'assicos}{35}
\contentsline {subsection}{\numberline {4.3.2}M\'etodos geom\'etricos}{37}
\contentsline {subsection}{\numberline {4.3.3}M\'etodos iterativos}{37}
\contentsline {subsubsection}{\numberline {4.3.3.1}Gradiente ascendente}{37}
\contentsline {subsubsection}{\numberline {4.3.3.2}Successive Over Relaxation}{41}
\contentsline {subsection}{\numberline {4.3.4}M\'etodos baseados em conjuntos ativos}{44}
\contentsline {subsubsection}{\numberline {4.3.4.1}Sub-problemas QP}{45}
\contentsline {subsubsection}{\numberline {4.3.4.2}Chunking}{46}
\contentsline {subsubsection}{\numberline {4.3.4.3}$\mathrm {SVM}^{light}${}}{46}
\contentsline {subsubsection}{\numberline {4.3.4.4}Sequential Minimal Optimization}{47}
\contentsline {chapter}{\numberline {5}A estrat\'egia de treinamento SVM-KM}{49}
\contentsline {section}{\numberline {5.1}Introdu\c c\~ao}{49}
\contentsline {section}{\numberline {5.2}Modelando o processo de estima\c c\~ao de limites entre classes}{50}
\contentsline {section}{\numberline {5.3}Generaliza\c c\~ao e an\'alise de desempenho}{52}
\contentsline {section}{\numberline {5.4}Estrat\'egias propostas}{53}
\contentsline {section}{\numberline {5.5}Simula\c c\~oes}{55}
\contentsline {section}{\numberline {5.6}Discuss\~ao}{56}
\contentsline {subsection}{\numberline {5.6.1}Tempo de inicializa\c c\~ao e execu\c c\~ao do KM}{56}
\contentsline {subsection}{\numberline {5.6.2}Tempo para SVM, tamanho do conjunto de treinamento e SVs}{57}
\contentsline {subsection}{\numberline {5.6.3}Tempo total e generaliza\c c\~ao}{58}
\contentsline {section}{\numberline {5.7}Conclus\~ao}{59}
\contentsline {chapter}{\numberline {6}O algoritmo de treinamento SVM-KM}{69}
\contentsline {section}{\numberline {6.1}Introdu\c c\~ao}{69}
\contentsline {section}{\numberline {6.2}Boosting}{70}
\contentsline {subsection}{\numberline {6.2.1}O algoritmo AdaBoost}{71}
\contentsline {section}{\numberline {6.3}O algoritmo de treinamento SVM-EDR}{73}
\contentsline {subsection}{\numberline {6.3.1}Repeti\c c\~ao Dependente do Error (EDR)}{73}
\contentsline {subsection}{\numberline {6.3.2}SVM-EDR}{75}
\contentsline {subsection}{\numberline {6.3.3}Entendendo e estimando $n_E$}{76}
\contentsline {subsection}{\numberline {6.3.4}SVM-EDR como um algoritmo de Boosting}{77}
\contentsline {section}{\numberline {6.4}Simula\c c\~oes}{80}
\contentsline {subsection}{\numberline {6.4.1}Primeiro exemplo}{80}
\contentsline {subsection}{\numberline {6.4.2}Segundo experimento}{81}
\contentsline {subsection}{\numberline {6.4.3}Terceiro experimento}{82}
\contentsline {section}{\numberline {6.5}Discuss\~ao}{83}
\contentsline {subsection}{\numberline {6.5.1}Hiperplanos de separa\c c\~ao}{83}
\contentsline {subsection}{\numberline {6.5.2}Converg\^encia}{84}
\contentsline {subsection}{\numberline {6.5.3}Tempo de treinamento}{85}
\contentsline {subsection}{\numberline {6.5.4}N\'umero de itera\c c\~oes e tamanho do conjunto Z}{85}
\contentsline {subsection}{\numberline {6.5.5}Taxa de generaliza\c c\~ao e n\'umero de vetores de suporte}{86}
\contentsline {section}{\numberline {6.6}Conclus\~ao}{86}
\contentsline {chapter}{\numberline {7}Conclus\~oes e trabalhos futuros}{99}
\contentsline {chapter}{Refer\^encias Bibliogr\'aficas}{101}
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